Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0955)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=3

http://functions.wolfram.com/07.22.03.0955.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 6}, z] == -((1/(5898454236675 z^4)) (64 (z (6129723600 - 5746615875 z - 42908065200 z^2 - 153223812000 z^3 + 93174701760 z^4 - 10613765376 z^5 + 374169600 z^6 - 4558848 z^7 + 16384 z^8) BesselI[0, Sqrt[z]]^2 - 4 Sqrt[z] (6129723600 - 4980400425 z - 17878360500 z^2 - 24499616400 z^3 + 21450426480 z^4 - 2585166336 z^5 + 92694528 z^6 - 1136640 z^7 + 4096 z^8) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] + (24518894400 - 16856739900 z + 28988484525 z^2 + 73633795200 z^3 + 113563749600 z^4 - 88134819264 z^5 + 10430049024 z^6 - 371902464 z^7 + 4550656 z^8 - 16384 z^9) BesselI[1, Sqrt[z]]^2)))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]